Affinity Laws

Pumps can operate at variable speeds during either steady operation or a transient event. Affinity laws (also called homologous laws) allow an estimation of the pump performance at speeds other than the design speed. For the Centrifugal (Rotodynamic) Pump model, these Affinity laws are used to model a variable speed pump during steady operation and to model the performance of a pump during any of the available transient models. For the Pump as Turbine model, these affinity laws are used to determine power generation or head loss while decoupled.

To a somewhat lesser degree, impeller diameter changes follow the same laws as speed changes. Substituting impeller changes for speed changes below can be used to see the effect of an impeller change or for a small impeller trim (larger trims deviate significantly from this estimation).

Before discussing the affinity laws, it should be noted that the affinity laws are an approximation. In many cases, pump manufacturers will have performance data for a number of speeds. This data should be used if available. When not available, the affinity laws can be used with an understanding that an approximation is being made.

Pump curves can generally be curve fit to a polynomial:

The speed ratio is defined in terms of the design impeller speed, N₁ and the desired operating speed N₂ as:

Affinity Laws

For the following ratios, subscript 1 represents the parameter from the defined curve (assumed to be at 100% speed). Subscript 2 represents the given parameter at the desired operating speed N2.

Flow rate -

Pump head -

Note: By default NPSHr will follow the same relationship as pump head rise. The speed ratio exponent used for NPSHr can be changed on the Configuration Data tab in the Pump Configuration window.

Power consumption -

Efficiency -

Application to Transients

During a transient event, the speed of the pump may change. In such cases, the affinity laws are used to adjust the head and power curves appropriately for the new speed. This is a process that often requires additional iteration.